Properties of Multiplication

In multiplication it makes no difference which of two number is considered to be the multiplier. The product is the same in either case. For example; 7 x 8 = 56 and 8 x 7 = 56. You will recognize that this fact is very similar to the commutative property in addition. Multiplication also possesses the Commutative property. This means that all the factors of a product can be arranged in any you want.

Does multiplication posses associative property? Take 2 x 3 x 8 x 7, you also have the same answer with 6 x 56 or 14 x 24 or 16 x 21 or 48 x 7. While this is not a proof that the associative law holds for multiplication, it does give a reason for thinking that it does. In advanced mathematics it can be proved that the associative law, as well as communicative law, applied to multiplication.

The two properties of mathematic, the commutative and associative properties, can be used to simplify multiplication in much the same way that you used them to simplify addition. Look to the example below:

4 x 3 x 19 x 25 =
(4 x 25) x 19 x 3 =
100 x 19 x 3 =
1900 x 3 = 5700

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